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Question

The minimum energy required to launch a satellite of mass m from the surface of earth of radius R in a cirulcar orbit at an altitude 2R is (mass of earth is M)

A

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B

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C

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D

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Solution

The correct option is D.

Energy of the satellite on the surface of earth is only the potential energy given by.

Ei=GmMR

The energy of satellite at a distance (2R + R) = 3R from center of earth is both potential as well as kinetic. Hence the total energy is given by,

Ef=GmM2(3R)=GMm6R

Energy required to launch the satellite is

E = EfEi=GMm6R(GmMR)=5GMm6R.


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